A method for simulating trajectories of particles undergoing Brownian motion in constricted domains is introduced. This method does not rely on discretization of the domain, and the computed trajectories are statistically equivalent to the trajectories of real Brownian particles. The stepsize is optimized over a continuum, making the method very efficient. The method is applied to study diffusion retardation in constricted, two-dimensional domains that represent idealized porous media. The effects of pore geometric parameters such as number of outlets per pore (nT), throat width (w), and throat length (z) are investigated. A retardation factor (Rp) is defined as the ratio of the average time required for a Brownian particle to pass through a constricted pore, to the average time required for a similar particle to pass through an unconstricted pore of equal length. For the class of pores studied, the empirical relation Rp ∼ [w/W]-β/nT, where W is the central pore body diameter, provides a reasonable fit to the simulation results. The exponent β increases with z/W.
Bibliographical noteFunding Information:
This work was supported in part by NIH Grant GM 26698, and in part by a predoctoral fellowship to RAS from the Paint Research Institute. The authors thank Andrea Mazel for typing the manuscript.